An Appreciation of Tony Marley (1940 - 2021)
The many kind things said about our dear Tony Marley are so right and appropriate, and I can only join all of the Department in celebrating his personal qualities, his teaching skills and his outstanding performance as department chair. Only a few of us, however, have mentioned his remarkable contributions to the mathematical side of probability. Let me see what I can do about this.
Tony concentrated most of his published work on the question of how people choose among things. This thoroughly psychological problem has two sides. What algorithm does a single person have that produces either a single choice, a choice of subsets, or a complete ranking of the presented possibilities? And, since people seldom seem to agree in their choices, how do choices vary over persons?
Of course gigabytes of data are collected for situations where choices are presented with a specified ranking already in place, such as for multiple choice testing questions or the Likert-type rating scales where numbers are attached to the choices.
But what about choice situations where we have little or no prior knowledge about which choices are best , worst, or in between? Tony and his research colleagues noted that people seem to prefer choosing these extremes much more than dealing with the in-betweens, and in fact one of limitations of rating scales is that extremes are often avoided, leading to somewhat mushy data outcomes. Perhaps we just need a good argument now and then.
Let me approach Tony’s work through my favourite A. A. J. Marley paper, which also happens to be his most cited. “Some probabilistic models of best, worst, and best-worst choices” appeared in the Journal of Mathematical Psychology in 2005 with joint authorship by Jordan Louviere, a professor in the School of Marketing of the Sydney University of Technology. The paper can be read (in principle and given enough time) by anyone who knows the basics of probabilities, i.e. that they are positive and add to one.
The usual psychometric models that we use to analyze data from multiple choice or rating scales are called “random utility models,” where the vague term “utility” means some non-negative level of desirability. Tony and Jordan showed that the random utility models in current use capture only a severely restricted idea of how choices can change across groups of people or for an individual over multiple choices. They explored the mathematical conditions that define random utility models versus a wider range of possibilities, and focussed on how best-, worst-, and joint best-worse decisions can be used to define a particular model choice.
Tony’s work has received rather more recognition in the econometric, market research and health assessment literature than in psychology. This seems a pity, but such is science. At least we have Tony to prove that psychology is not the worst choice for a mathematician of his calibre.